Atkin-Lehner |
2- 5+ 11- 61+ |
Signs for the Atkin-Lehner involutions |
Class |
53680u |
Isogeny class |
Conductor |
53680 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
138240 |
Modular degree for the optimal curve |
Δ |
-544863577702400 = -1 · 228 · 52 · 113 · 61 |
Discriminant |
Eigenvalues |
2- 0 5+ 4 11- 0 2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,20237,-182862] |
[a1,a2,a3,a4,a6] |
Generators |
[254:4620:1] |
Generators of the group modulo torsion |
j |
223770153205431/133023334400 |
j-invariant |
L |
6.2304753253402 |
L(r)(E,1)/r! |
Ω |
0.30361680377789 |
Real period |
R |
3.4201419068472 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.9999999999996 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
6710a1 |
Quadratic twists by: -4 |